Python module installation does not work
If you can start command prompt, and get python34 REPL, and import numpy and tables without errors, there's little reason that Blender's python console can't do the same.

Determine which python executable is used

Run this bit of code in two different locations. First from command prompt python interpreter and then from Blender's python console.

import sys
print(sys.path)
print(sys.executable)


You might notice that Blender isn't finding the same python executable. If they are different, this can explain why imports are failing. If they are the same that's a good thing. Half the battle is won!

Test your Python separately first.

On windows make sure the C:\Python34; is at the start of the PATH line, when you type in python into command prompt you'll want 3.4(.1+) to launch. (At least, I've had success with that and numpy1.8 on windows)

You should also be able to import numpy from command prompt without errors

Python 3.4.1 (v3.4.1:c0e311e010fc, May 18 2014, 10:38:22) &lt;edited&gt;
Type "help", "copyright", "credits" or "license" for more information.
&gt;&gt;&gt; import numpy
&gt;&gt;&gt; # also try the other important imports, stuff must work from here too


If you get errors from this python interpreter, forget about blender and fix the errors first. Once fixed, blender too will be able to use the libraries.

If you still have the python directory inside Blender's folder now is a good time to rename it to _python.

The Blender warning when you rename/remove its own python folder


  Warning: bundled python not found and is expected on this platform. 


is just that, a warning. Telling you that Blender looked in the directory where it keeps Python and couldn't find it, that's OK. It's perfectly fine to use your local Python34 installation, on windows I prefer to use it that way. Pasting around libraries into scripts/modules folder obviously didn't work, I suggest removing the files you added there to prevent them from interfering with imports. 

For sverchok we found it was necessary to install Numpy 1.8 and Python3.4.1, and did a small write-up. I won't reproduce here because this is bordering on off-topic.

Forcing Blender to use your local system Python3.4.x

When Blender is forced to use the system's local python 3.4.x it hoists some paths of its own into the global namespace at runtime, to allow for importing bpy and all other blender modules. Apart from that the py3.4 runtime is entirely your system's.

If your imports are failing inside Blender, even though it uses the local python3.4, it is likely because you moved libraries into scripts/modules/.. or one of the other paths listed in sys.path. Python is going to look in the sequence given by sys.path, it iterates over the list, to find an import that matches your import statements. if Python finds anything before it hits 'C:\Python34\lib\site-packages` that will be tried first and only.

You should have a nice directory with all your python3.4 libraries like

C:\Python34\lib\site-packages\numpy
C:\Python34\lib\site-packages\scipy
# etc